Question

Which expression is equivalent to (2mn)^4/6m^-3n^-2? Assume .m=0,n=0

Answer 1

Given expression:$\frac{(2mn)^4}{6m^{-3}n^{-2}}$.

$\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c$

$\left(2mn\right)^4:\quad 2^4m^4n^4$

$=\frac{2^4m^4n^4}{6m^{-3}n^{-2}}$

$=\frac{2^4m^4n^4}{2\cdot \:3m^{-3}n^{-2}}$

$=\frac{2^3m^4n^4}{3m^{-3}n^{-2}}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}$

$\frac{m^4}{m^{-3}}=m^{4-\left(-3\right)}=m^7$

$=\frac{2^3m^7n^4}{3n^{-2}}$

$\frac{n^4}{n^{-2}}=n^{4-\left(-2\right)}=n^6$

$=\frac{2^3m^7n^6}{3}$

$=\frac{8m^7n^6}{3}$

Therefore, correct option is first option $\frac{8m^7n^6}{3}.$

Answer 2

8m^7n^6
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